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August 2014 Nonparametric ridge estimation
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman
Ann. Statist. 42(4): 1511-1545 (August 2014). DOI: 10.1214/14-AOS1218


We study the problem of estimating the ridges of a density function. Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data. We show that, under mild regularity conditions, the ridges of the kernel density estimator consistently estimate the ridges of the true density. When the data are noisy measurements of a manifold, we show that the ridges are close and topologically similar to the hidden manifold. To find the estimated ridges in practice, we adapt the modified mean-shift algorithm proposed by Ozertem and Erdogmus [J. Mach. Learn. Res. 12 (2011) 1249–1286]. Some numerical experiments verify that the algorithm is accurate.


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Christopher R. Genovese. Marco Perone-Pacifico. Isabella Verdinelli. Larry Wasserman. "Nonparametric ridge estimation." Ann. Statist. 42 (4) 1511 - 1545, August 2014.


Published: August 2014
First available in Project Euclid: 7 August 2014

zbMATH: 1310.62045
MathSciNet: MR3262459
Digital Object Identifier: 10.1214/14-AOS1218

Primary: 62G05 , 62G20
Secondary: 62H12

Keywords: Density estimation , manifold learning , Ridges

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 4 • August 2014
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